Experimental and Numerical Evaluation of Shear Strength of Directly and Indirectly Loaded Flanged Recycled Self-Compacted Reinforced Concrete Deep Beams

Hindawi Journal of Engineering Volume 2020, Article ID 3462010, 20 pages https://doi.org/10.1155/2020/3462010

Research Article Experimental and Numerical Evaluation of Shear Strength of Directly and Indirectly Loaded Flanged Recycled Self-Compacted Reinforced Concrete Deep Beams

Thamer Hussein Amer Alhussein and Jamal Abdul Samad Khudhair

Department of Civil Engineering, College of Engineering, University of Basrah, Basrah 61004, Iraq

Correspondence should be addressed to amer Hussein Amer Alhussein; [email protected]

Received 19 April 2020; Revised 27 July 2020; Accepted 4 August 2020; Published 24 August 2020

Academic Editor: Hamzeh F. Haghshenas

Copyright © 2020 amer Hussein Amer Alhussein and Jamal Abdul Samad Khudhair. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Experimental and numerical investigations of the behavior of directly and indirectly loaded flanged reinforced concrete (RC) deep beams cast with self-compacted concrete (SCC) containing recycled concrete as coarse aggregate (RCA) were conducted in this research. Seventeen RC deep flanged beams were designed to fail in shear. ese beams were divided into three groups: twelve indirectly loaded beams without shear reinforcement; three directly loaded beams without stirrups; and two indirectly loaded beams with vertical stirrups. ese beams were also classified according to the RCA ratio and shear span-to-effective depth (a/d) ratio, which will be detailed later. e RCA ranged from 0% to 75%, while the a/d ratio was taken as 1.0, 1.35, and 1.7. Ex- perimental results show that the use of RCA reduces the cracking and ultimate capacities, and this finding complies with the conclusions of several research studies in the literature as will be detailed later. It was observed that beams with higher RCA exhibited higher deflection, strain, and crack width. Furthermore, by increasing the a/d ratio, the ultimate load was decreased due to the lower contribution of arch action shear transfer in the beam. A web reinforcement spaced at 100 mm and 50 mm increases the ultimate load by 35% and 48%, respectively. Strut and tie model (STM) presented by the American Concrete Institute (ACI) 318-14 and the American Association of State Highway and Transportation Officials (AASHTO LRFD 2012) was used to predict the ultimate shear capacity of the beams. STM predicted lower beam capacity than the experimental result. e ultimate strength calculated using ACI318-14 and AASHTO LRFD 2012 was on average 38% and 52% lower than the experimental data, respectively, which reflects the conservative nature of this approach. Finally, 3D finite element models were created to investigate the responses of the beams. e FE results showed very good agreement with the experimental data, where FE-predicted shear capacities were on average 9% higher than the experimental results.

1. Introduction RCA on the shear strength of RC beams. It is suggested that a 20% reduction is applied to the shear strength equations of Waste materials (WM) resulting from the demolition of conventional reinforced beams when RCA is incorporated in tremendous concrete structures that have reached the end of the concrete. Wardeh and Ghorbel [2] presented an ex- their lifespan have negatively impacted the environment. perimental study on the shear behavior of beams without Concrete manufactured with WM as partial replacement of transversal reinforcement made with NA concrete and 100% natural aggregate (NA) represents a more sustainable so- RA concrete. e experimental conclusions showed that, for lution to reduce further wasting materials and to minimize the same class of compressive strength, tensile strength, and the consumption of natural resources. Many researchers fracture energy, the shear strength of RA concrete is weaker have eﬃciently used recycled aggregate (RA) from concrete than that of NA concrete. waste as a partial replacement of the NA. Rahal and Alrefaei Segregation in concrete structures is a major challenge, [1] experimentally investigated the eﬀects of the usage of especially in elements that have dense reinforcement. 2 Journal of Engineering

erefore, SCC is a reliable solution in concrete technology literature have been conducted to investigate the response for this issue. e workability characteristic of SCC allows of deep beams made with self-compacted RA concrete. concrete to fill molds even in densely reinforced elements us, this research tries to fill the gap and present a with no segregation under the effect of its weight. Roy et al. thorough study that includes an experimental, code-based, [3] investigated the fresh and mechanical properties of SCC and FE evaluation to investigate the responses of such using locally available materials and incorporating different elements. Furthermore, studying the effect of indirect water-cement ratios (w/c). e experimental results revealed loading conditions on the response of RASCC deep beams that both compressive and tensile strengths were increased is underdocumented even in international standards like with the reduction of the w/c ratio. Revilla-Cuesta et al. [4] ACI and AASHTO. erefore, this research presents a studied the properties of SCC with RCA, as well as related detailed study and offers an experimentally quantified results on the fresh state (workability, rheology), the approach that can be utilized to implement the effect of hardened state (compressive strength, splitting tensile, and indirect loading conditions on the response of deep beams. flexural strength; modulus of elasticity, density, and po- Another important feature of this research is the combi- rosity), durability (resistance to aggressive agents), long- nation of using deep beams prepared using RCA as a partial term properties of concrete (shrinkage, creep), and struc- replacement of NA and utilizing the SCC technique. is tural elements manufactured with SCC containing RCA. e combination produces more sustainable structural ele- results confirmed that the incorporation of RCA can pro- ments and eliminates construction efforts. duce a suitable recycled aggregate self-compacted concrete (RASCC), based on careful designs essential for desired performance. 2. Strut and Tie Model Deep beams have very significant applications in the Structural standards like ACI 318-14 and AASHTO LRFD area of engineering structures. Deep beams are structural (2012) have adopted the STM for predicting the strength of elements loaded on one face and supported on the other the deep beams in 2002 and 1994, respectively. e model face so that compression struts can develop between the idealized by a hypothesis truss, which consists of struts and loads and the supports [5]. Defining beams as deep beams is ties connected at nodes. e struts represent the compres- controlled by satisfying geometric and/or loading sion members, while the ties are the tension members. conditions. Details of this approach are thoroughly presented in ACI e ACI code 318-14 has stated that a beam is con- 318-14 and AASHTO LRFD (2012). e STM analogy for the sidered as a deep beam when either its clear span is within studied beams in this research is shown in Figure 1. four times the overall member depth or the applied con- In both ACI 318-14 and AASHTO LRFD 2012, it is clear centrated load acts within a distance of two times the that the methodology and the determination of the internal member depth from the face of the support [5]. Nonlinear forces are the same where (1) explains the design criteria of strain distributions in deep beams are caused by sudden both standards, (2) calculates nominal compressive strength changes in geometry or loading. is nonlinear strain of a strut, (3) determines the nominal tensile strength of a tie, distribution is violating the assumption of linear strain and (4) gives the nominal compressive strength of a nodal distribution in slender beams, and the assumption of plane zone. e main difference between these two standards is sections remains plane. In other words, shear deformations about determining the effective stress of the struts, ties, and in deep beams are more significant and dominate the nodes. erefore, Table 1 shows a summary of the effective behavior of the element in comparison with slender beams. stress for each element in these codes. erefore, the classical beam theory is no longer applied to According to ACI 318-14 and AASHTO LRFD 2012, the deep beams and cannot be used to determine the internal ultimate shear strength of deep beams must be greater than state of stress. STM presented by the ACI code 318-14 and or equal to the factored applied shear forces as presented in the AASHTO 2012 was used to predict the ultimate shear capacity of the tested beams. e STM is considerably ΦFn ≥ Fu, (1) conservative and represents lower-bound strength limit states [5, 6]. Razzaq et al. [7] presented experimental where Fu is the largest force in that element for all load verification of STM for RC deep beams under various types combinations considered and Fn is the minimum nominal of loadings. Test results indicated that each beam carried strength of struts, ties, and nodes: loads greater than the STM design load. In other words, the e nominal compressive strength of a strut, Fnstrut, is STM is conservative, which gives the designers wide calculated by flexibility. Also, finite element analysis (FEA) was used to Fn � fc Ac + As′ fs′. ( ) study the behavior of deep beams under direct and indirect strut eff_strut ∗ strut ∗ 2 loading conditions, as suggested by many research studies e nominal tensile strength of a tie, Fn , is calculated in the literature [2, 8]. tie by Although deep beams are widely used in construction projects, the evaluation of ultimate strength is still less Fntie � fy ∗ Astie. (3) documented and limited, with a lot of uncertainties about understanding the behavior and the failure mechanism of e nominal compressive strength of a nodal zone (CCC these elements. A limited number of research studies in the and CCT), Fnnode, is calculated by Journal of Engineering 3

F u 3.1. Materials. e properties of the materials used in the preparation of the samples are described herein. Conven- Nodal Zone tional Portland cement type I that complies with the Iraqi lbt speciﬁcation number (5/1984) [9], ASTM C150 [10], C109 [11], and BS EN197 [12] was used. Physical and chemical Compresion Interior strut reinforcement bars characteristics of the coarse and ﬁne aggregate were tested w st according to ASTM C33 [13]. RCA was obtained from waste w c

sb d materials of crushed concrete cubes. In terms of particle size h θ° distribution, the RCA grading complied with the same speciﬁcation for normal coarse aggregate. Potable water was

t Tension reinforcement bars utilized for both mixing and curing of the samples. In this w work, the superplasticizer used is a new generation of

lbb Tie modiﬁed polycarboxylic ether, which is known commer- a a cially as Glenium 51. is material is compatible with all L c/c Portland cement types and free from chlorides and complies

Fu/2 Fu/2 with ASTM C494 [14]. Superplasticized concrete exhibits better workability without the occurrence of segregation. It Figure 1: Strut and tie model (STM). also provides enough time for mixing, casting, and finishing the final concrete surface. A limestone powder (LSP) was used to acquire the SCC by increasing the amount of ce- mentitious material content (cement + filler). e physical Table 1: Summary of effective stress for prediction ultimate properties of the constituents are presented in Table 2. Steel strength of deep beams using STM by ACI318-14 and AASHTO reinforcing deformed bars were used for the longitudinal LRFD 2012. reinforcement and stirrups. ree specimens of each size were tested according to the ASTM A615 [15]. e prop- Element ACI 318-14 AASHTO LRFD 2012 erties of reinforcing bars are presented in Table 3. After f′c f c . + . f′c Strut 0.85 ∗ (0.6) ∗ ′ /0 8 170 ∗ ε1 ≤ 0 85 several trial mixes, the mix proportions shown in Table 4 Tie fy fy were adopted in this study. CCC node 0.85 ∗ (1.0) ∗ f′c 0.85 ∗ (0.8) ∗ f′c CCT node 0.85 ∗ (0.85) ∗ f′c 0.75 ∗ (0.8) ∗ f′c 3.2. Details of the Beams. In this study, seventeen RASCC a d Fnnode � fceff_node ∗ Acnode. (4) T-beams were designed to fail in shear with different / ratios (1.0, 1.35, and 1.7). Four mixes were prepared with Notation: fceff_strut and fceff_node: effective stress in a strut different RCA replacement ratios (0%, 25%, 50%, and 75%). and a node, respectively, given in Table 1; fc′: specified Out of fourteen indirectly loaded beams, twelve were pre- compressive strength of concrete; fy: specified yield strength pared without web reinforcement, while two were cast with of tensile reinforcement; ε1: principle tensile strain in different amounts of the stirrup (spaced at 50 mm and concrete; CCC: node formed by three or more intersecting 100 mm, respectively). e other three beams, which rep- struts; CCT: node formed by two or more intersecting struts resented the control beams, were directly loaded with the and a tie; Acstrut: the cross-sectional area at the end of the same longitudinal reinforcement details with no stirrups. All strut; As′: the area of compression reinforcement along strut beams have the same cross section with a web thickness bw of length;fs′: the compression reinforcement stress at the 150 mm, flange width bf of 450 mm, flange depth hf of nominal axial strength of the strut; Astie: the area of tie 100 mm, and overall beam depth of 350 mm. e details of reinforcement; Acnode: the area of the section through the the T-beams are presented in Tables 5–7 and Figures 2–4. nodal zone perpendicular action line of the resultant force on the section. e STM was used to predict the ultimate load capacity 3.3. Concrete Mixing Procedure. e mixture was prepared of studied deep beams. All the parameters required by STM using a laboratory mixer with a capacity of 0.1 m3. e same to determine the capacity were taken from the experimental mixing procedure was maintained throughout this study to tests. However, it is important to mention that STM does not obtain the optimum effectiveness of superplasticizer and take into consideration the loading condition on the beam total dispersion of the particles, as suggested by some re- (i.e., direct and indirect loading), which is one of the searchers in the literature [3, 16]. is procedure is sum- drawbacks of this method. More details of STM results are marized as follows: presented later in this article. (1) Cement, limestone, and aggregate were placed and mixed for one minute. 3. Experimental Program (2) 80% of mixing water was gradually added to the e experimental work was carried out in the laboratories of mixture while maintaining the mixing process for the Civil Engineering Department, University of Basra. another minute. 4 Journal of Engineering

Table 2: Physical properties of constituents. Coarse aggregate Test details Fine aggregate Limestone powder (LSP) NCA RCA Speciﬁc gravity 2.63 2.66 2.39 2.4 Moisture content (%) 1.00 0.55 — — Dry density (g/cm3) 1.72 1.69 — — Water absorption (%) 1.20 0.84 5.5 5

Table 3: Properties of reinforcing bars. Test results Bar size (mm) Yield stress (N/mm2) Ultimate strength (N/mm2) Elongation (%) 10 482 595 12 12 516 647 13 16 530 677 12

Table 4: Concrete mix constituents per cubic meter. 3.4. Fresh and Hardened Properties of the Mixture. Cement LSP Water Sand Gravel SP According to the European Guidelines for SCC (EFNARC, (kg) (kg) (kg) (kg) (kg) (liter) 2005), three characteristics represent the fresh SCC: filling ability, passing ability, and segregation resistance [17]. 379 162 167 755 944 5 erefore, several tests were conducted to ensure that the SCC mix meets these requirements, as shown in Figure 5 and Table 8. e mechanical properties of the SCC mixture were determined. In particular, the compressive strength of cubes Table 5: Indirectly loaded beams (12 beams). (fcu), splitting tensile strength (ft), and modulus of elasticity Beam SN a/d RCA (%) (Ec) were tested using three specimens for each test, and the G1TB 1.0 average value was taken as presented in Table 9. G2TB 1.35 0 25 50 75 G3TB 1.7 3.5. Casting of Beams. Wooden molds were used in the fabrication of the beams. e inside of the forms was lu- bricated before placing the reinforcement cage in the des- Table 6: Directly loaded beams (3 beams). ignated position. Under the influence of its weight, the Beam SN a/d RCA (%) concrete mixture was easily placed and leveled. e beams were moist-cured as per ACI 318-14 requirements for seven DG1TB3 1.0 DG2TB3 1.35 50 days and then stored in the laboratory for testing. DG3TB3 1.7 3.6. Testingof Beams. Before conducting the tests, the beams were painted to facilitate tracing the cracks. Aluminum discs with a 10 mm diameter and a central hole of 1.5 mm di- Table 7: Indirectly loaded beams with stirrup (2 beams). ameter were used to measure the strain in the concrete. e Beam SN a/d RCA (%) Spacing (mm) discs were positioned and attached to concrete by utilizing G1TB3S 100 an epoxy resin, as shown in Figure 6. e typical arrange- 1.0 50 G1TB3S 50 ment, experimental setup, and loading configuration are shown in Figure 7. Universal Testing Machine (UTM) with a capacity of 2000 kN was used to apply the load. Midspan (3) e superplasticizer was dissolved in the remaining deflection, concrete strain, and crack width were measured 20% of mixing water and then slowly added to the during the tests. Also, the inclined cracking load and ulti- mixture, while the mixing was performed for another mate load were recorded for each beam. minute. (4) e mixing was maintained for another three 4. Experimental Results and Discussion minutes. 4.1. Crack Pattern. All tested beams failed in shear with no (5) e mixture was rested for three and a half minutes. failure under load application or over supports. Also, the (6) Finally, the mixture was remixed for another half main bars were properly placed to prevent any anchorage minute and released for executing the fresh concrete failure. e first set of cracks that appeared due to loading tests and casting the samples and beams. comprised small flexure cracks at the bottom of the midspan Journal of Engineering 5

Top view Front view B 950mm A 150mm 250mm 150mm 250mm 150mm Ø10mm @175mm 150mm

2Ø12mm 2Ø10mm 150mm

350mm 4Ø16mm 150mm B A

(a) (b)

Figure 2: Indirectly loaded G1TB.

Top view Front view B 950mm 150mm 325mm 325mm 150mm 150mm 100mm 2Ø12mm 2Ø10mm

150mm 4Ø16mm 250mm 150mm B

(a) (b)

Figure 3: Directly loaded DG1TB.

450mm 450mm 150mm 150mm 150mm

4Ø16mm 100mm

100mm 4Ø12mm

6Ø10mm

250mm 4Ø16mm 4Ø16mm 2Ø12mm 150mm Sec. A-A Sec. B-B

(a) (b)

Figure 4: Cross section details. of the beam. With further loading, an inclined crack oc- in shear. For deep beams without web reinforcement, the curred at shear zone approximately at the center of the inclined crack extended toward top and bottom with no inclined strut. en, the main shear crack started to appear significant increase in crack width and suddenly failed in at a location close to the beam middepth (center of the strut) shear. is behavior is attributed to the absence of web with the same inclination of the strut. reinforcement, especially for deep beams with small shear A further increase in the load caused a small rise in crack span–to–effective depth (a/d) ratio. is finding complies width and formed another inclined crack parallel to the first with the past research studies, which observed that RC crack, and then the shear cracks extended toward the bottom beams with shear reinforcement fail with a diagonally and top of the beam, widened, and propagated up to failure cracked area, while those without shear steel fail with single 6 Journal of Engineering

V-Funnel test

Slump flow

(a) (b)

L-Box test Slump Test

Figure 5: L-box, v-funnel, slump ﬂow, and T50 tests.

Table 8: Properties of fresh RASCC. EFNARC Guideline T500 (sec) EFNARC Guideline RCA (%) Slump ﬂow (mm) Min Max Min Max 0 700 650 800 2.66 2 5 25 680 650 800 2.70 2 5 50 660 650 800 2.72 2 5 75 650 650 800 3.02 2 5 EFNARC Guideline EFNARC Guideline RCA (%) V-funnel (sec) L-box Min Max Min Max 0 8.27 8 12 0.94 0.8 1.00 25 8.40 8 12 0.94 0.8 1.00 50 8.56 8 12 0.93 0.8 1.00 75 9.41 8 12 0.89 0.8 1.00

Table 9: Properties of hardened RASCC.

Mix with RCA (%) Compressive strength (fcu) (MPa) Tensile strength (ft) (MPa) Modulus of elasticity (Ec) (MPa) 0 42.20 3.96 27510 25 40.40 3.94 26950 50 36.60 3.43 25740 75 32.40 3.12 24110 Journal of Engineering 7

50mm A

50mm B C D Dial gauge

Figure 6: Arrangement of gauges in tested beams.

300mm

h f h h f h

l n bw l n bw

(a) (b)

Figure 7: Instrumentation and testing procedure of the beams. major diagonal crack [18, 19]. e failure happened in the Figure 11 illustrates a comparison between inclined flanged deep beam when the major diagonal crack penetrates cracking loads (Pcr) and ultimate loads (Pu) for indirectly the flange area. e crack patterns of tested beams after loaded beams with different RCA ratios. e inclined cracking failure are shown in Figures 8–10. load is also affected by the RCA percentage because the tensile strength of concrete decreased with the increase in RCA. For directly loaded T-deep beam with 50% RCA 4.2. Inclined Cracking and Ultimate Loads of RASCC Beams (DG1TB3, DG2TB3, and DG3TB3), the ratio of inclined cracking to ultimate loads was 31%, 33%, and 33%, re- 4.2.1. Effect of RCA Replacement Ratio. Inclined cracking spectively, as shown in Table 12. Finally, the directly loaded and ultimate loads are listed in Tables 10–12. e inclined flanged deep beams exhibit higher load capacity than the cracking load is defined as the load at which the first major indirectly loaded flanged deep beams because of the arch inclined crack appears in the shear span. For the same a/d action mechanism. Indirectly loaded flanged deep beams are ratio, the ratios of inclined cracking to ultimate load for weaker than directly loaded deep beams; this is due to the indirectly loaded beams ranged from 26% to 36%, with an lower arch action developed in indirectly loaded RC deep average value of 32%, as illustrated in Table 10. For beams in beams [20]. the first group, G1TB2, G1TB3, and G1TB4, where the Based on experimental results, the average ultimate replacement ratio is 25%, 50%, and 75%, respectively, the capacity of directly loaded deep beams was 23% higher than ultimate load was decreased by 14%, 38%, and 42%, re- the ultimate capacity of indirectly loaded beams. is spectively. For beams in the second group, G2TB2, G2TB3, modification factor, extracted from experimental data, can and G2TB4, with replacement ratios of 25%, 50%, and 75%, be applied to the STM method to account for different respectively, the ultimate load was decreased by 21%, 40%, loading conditions as the current STM does not account for and 46%, respectively. For beams in the third group, G3TB2, such effect. G3TB3, and G3TB4, with replacement ratios of 25%, 50%, and 75%, respectively, the ultimate load was decreased by 2%, 9%, and 20%, respectively. e decrease in ultimate 4.2.2. Effect of a/d Ratio. e magnitudes of the shearing loads of the beams is attributed to the reduction in com- stress and flexural stress affecting the inclined cracking and pressive strength by increasing the RCA. the subsequent failure of RC deep beams are considered as a 8 Journal of Engineering

G3TB4

G3TB3

(a) (b)

Figure 8: Crack pattern for indirectly loaded beams without shear reinforcement.

G1TB3S100 G1TB3S50

(a) (b)

Figure 9: Crack pattern for indirectly loaded beams with shear reinforcement.

DG3TB3 DG1TB3

(a) (b)

Figure 10: Crack pattern for directly loaded beam (DGTB). function of a/d ratio [8]. e distribution of stresses in the for directly loaded beams, the inclined cracking and ultimate deep beams after forming inclined crack revealed a ten- loads were increased by 29% and 33%, respectively. Further, dency toward the arch action. However, no pure arch action inclined cracking and ultimate loads for the same RCA were was formed because the force in the tension steel rein- increased by 7% and 10% for indirectly loaded beams, while forcement is not constant along the span [21]. From Ta- the increase was 15% and 20% for directly loaded beams bles 10 and 12, it can be observed that the increase in the when a/d ratio reduced from 1.35 to 1.0. is increase in inclined cracking and ultimate loads is achieved by re- inclined cracking and ultimate loads is due to the higher ducing a/d ratio. contribution of arch action shear transfer in beams with a For instance, the inclined cracking and ultimate loads of lower a/d ratio, which conﬁrms other research ﬁndings in deep beams with RCA of 50% were increased by 19% and the literature [19, 22]. Figure 12 shows a comparison be- 15% for indirectly loaded beams, respectively. Meanwhile, tween inclined cracking loads (Pcr) and ultimate loads (Pu) Journal of Engineering 9

Table 10: Inclined cracking and ultimate loads for indirectly loaded beams. Reduction due to Load (kN) Beams a/d RCA (%) RCA (%) Pcr/Pu (%) Reserved strength Pu − Pcr/Pcr (%) Inclined cracking Pcr Ultimate Pu Pcr (%) Pu (%) G1TB1 0 210 740 — — 28 252 G1TB2 25 200 640 5 14 31 220 1.0 G1TB3 50 160 460 24 38 35 188 G1TB4 75 130 430 38 42 30 231 G2TB1 0 200 700 — — 29 250 G2TB2 25 200 550 0 21 36 175 1.35 G2TB3 50 150 420 25 40 36 180 G2TB4 75 100 380 50 46 26 280 G3TB1 0 141 440 — — 32 212 G3TB2 25 140 430 1 2 33 207 1.7 G3TB3 50 135 400 4 9 34 196 G3TB4 75 115 350 18 20 33 204

Table 11: Inclined cracking and ultimate loads for indirectly loaded beams with diﬀerent amount of web reinforcement. Load (kN) Beams a/d RCA (%) Pcr/Pu (%) Reserved strength Pu − Pcr/Pcr (%) Inclined cracking Pcr Ultimate Pu G1TB3S100 165 620 27 276 1.0 50 G1TB3S50 170 680 25 300

Table 12: Inclined cracking and ultimate loads for directly loaded RCASCC beams. Load (kN) Beams a/d RCA (%) Pcr/Pu (%) Reserved strength Pu − Pcr/Pcr (%) Inclined cracking Pcr Ultimate Pu DG1TB3 1.0 200 640 31 220 DG2TB3 1.35 50 170 510 33 200 DG3TB3 1.7 143 430 33 201

800 700 RCA 50% 600 600 500 400 400 300

Load (kN) 200 Load (kN) 200 100 0 G1TB3 DG1TB3 G2TB3 DG2TB3 G3TB3 DG3TB3 0 Inclined cracking Pcr Ultimate Pu a/d (1.0) a/d (1.35) a/d (1.7)

G1TB1 G1TB3 Cracking load Pcr G1TB2 G1TB4 Ultimate load Pcr

Figure 11: Comparison between inclined cracking loads and ul- Figure 12: Comparison between inclined cracking loads and ultimate loads for indirectly loaded beams with different RCA. timate loads of directly and indirectly loaded beams with different a/d ratios. for directly and indirectly loaded beams with different a/d ratios. For beams prepared with the same RCA and a/d ratio, 4.2.3. Effect of Web Reinforcement. Although the presence of Figure 12 shows that the directly loaded beams developed vertical web reinforcement does not affect the first inclined higher cracking strength and ultimate strength compared cracking loads, it affects the crack width. Further, the ulti- with indirectly loaded beams. mate load capacity is significantly affected by the existence of 10 Journal of Engineering web reinforcement, as shown in Table 11 and Figure 13. For 800 example, the presence of vertical web reinforcement in 700 indirectly loaded flanged deep beams G1TB3S100 causes an 600 increase in ultimate loads of about 35% as compared with 500 beams without web reinforcement, GTB. Also, the ultimate 400 300 load capacity of G1TB3S50 was increased by 48% compared Load (kN) with GTB. is finding complies with [21, 22]. Table 11 200 shows that, for the same a/d ratio, the ratio of inclined 100 0 cracking to ultimate loads was 27% and 25% for the indi- G1TB3 G1TB3S100 G1TB3S50 rectly loaded flanged deep beam with shear reinforcement of a/d (1.0), RCA 50% G1TB3S100 and G1TB3S50, respectively. Cracking load Pcr Ultimate load Pcr

4.2.4. Reserved Strength. e reserved strength is defined as Figure 13: Comparison between inclined cracking loads and ul- the difference between the ultimate load and diagonal timate loads for indirectly loaded beams with different amount of cracking load divided by the diagonal cracking load web reinforcements. expressed as a percentage [8, 18]. e reserved strength of the tested beams is listed in Tables 10–12. It was seen from 800 the test results that the reserved strength of the indirectly loaded beams is lower than the reserved strength of the directly loaded beams by 9%. Beams with web reinforcement exhibited 53% reserved strength higher than those without 600 web reinforcement. e importance of reserved strength is that a safe margin of the capacity is reserved after cracking so that no immediate failure will happen instantaneously after 400 cracking [8, 22]. Load (kN)

200 4.3. Deflection. From the experimental data, load-midspan G1TB deflection curves for all tested beams are shown in Figures 14–18. It can be noticed that the formation of the first major inclined crack significantly reduces beam stiffness 0 and tends to cause a change in the slope of the curves. e 0 246810 higher replacement ratio of RCA results in slightly higher Deflection (mm) deflection. e increase in deflection for T-beams with in- 0% 50% creasing the replacement ratio of RCA is attributed to the 25% 75% lower modulus of elasticity and compressive strength of Figure 14: Load deflection curve for G1TB. RCA compared to NA specimens. e presence of web reinforcement is also affected by reducing the midspan deflection at the same loading. e amount of deflection is increased considerably with the increase of span–effective 800 depth ratio.

600 4.4. Concrete Strain. Strain in concrete was measured in several locations along the inclined strut that connects the applied load and the support as shown in Figure 6. e strain 400 reading was profoundly aﬀected by the presence of any crack within or near strain gauge, because the strain measure- Load (kN) ments represent the combination of concrete strain and 200 crack width. erefore, strain-load plots were constructed G2TB up to a load that is slightly higher the cracking load as depicted in Figures 19–24. From the experimental data, it 0 can be concluded that the beams made with RA concrete 0 246810 have higher concrete strains than those made with NA. e Deflection (mm) concrete strains slightly decrease with the increase in web reinforcement. From the test results and for the same RCA 0% 50% ratio, the measured strain was higher when a/d increased as 25% 75% shown in Figures 19–22. Figure 15: Load deﬂection curve for G2TB. Journal of Engineering 11

500 700

600 400 500 300 400

200 300 Load (kN) Load (kN) 200 100 G3TB 100 DGTB3

0 0 0 24681012 0 12345678 Deflection (mm) Deflection (mm)

0% 50% DG1TB3 25% 75% DG2TB3 DG3TB3 Figure 16: Load deﬂection curve for G3TB. Figure 18: Load deﬂection curve for DGTB3. 800 300

600 250

200 400 150 Load (kN) Load (kN) 100 200 G1TB3S 50 G1TB1

0 0 0 24681012 Deflection (mm) 5.0 E – 5 1.0 E – 4 1.5 E – 4 2.0 E – 4 2.5 E – 4 3.0 E – 4 0.0 E + 0 S = 100mm –1.0 E – 4 –5.0 E – 5 Strain S = 50mm A C Figure 17: Load deﬂection curve for G1TB3S. B D

Figure 19: Strain of G1TB1. 4.5. Inclined Crack Width. Experimental results showed that the crack width increases with the increase of the RCA same beam with stirrup spaced at 50 mm showed the replacement ratio as presented in Figure 25. is behavior is smallest crack width among all the studied cases. e ad- due to the lower modulus of elasticity of concrete with a dition of web reinforcement causes an increase in the higher replacement ratio. It was observed that, at the RCA stiffness of the beam compared to the beam without stirrups. ratio (0% and 50%) and with the absence of web rein- Furthermore, the presence of web reinforcement causes a forcement, the crack width became larger as the shear span delay in crack formation. ratio (a/d) increases, as illustrated in Figure 26. A comparison between the crack width values of RASCC beams 5. Finite Element Analysis and different values of web reinforcement (without stirrups, spaced at 50 mm, and spaced at 100 mm) is shown in Fig- Detailed 3D finite element models of RC deep beams were ure 27. It can be observed that beams without web rein- implemented in this study. e FE models were created forcement showed the highest crack width among the using FE commercial software package Abaqus [23] to studies discussed herein. Also, the crack width showed a predict ultimate shear capacity and comparing the results tendency to decrease with decreasing the spacing of the with experimental data. FE models were refined and cali- stirrups. For instance, the beam with a/dof 1.0, RCA of 50%, brated using experimental data to extend them to predict and stirrups spaced at 100 mm showed lower crack com- other parameters that were not measured during the ex- pared to beam without web reinforcement. Furthermore, the perimental program. e models were subjected to direct 12 Journal of Engineering

250 250

200 200

150 150

100

Load (kN) 100 Load (kN)

50 50 G1TB3 DG1TB3 0 0 1.0 E – 4 2.0 E – 4 3.0 E – 4 4.0 E – 4 5.0 E – 4 0.0 E + 0 –1.0 E – 4 1. E – 04 2. E – 04 3. E – 04 4. E – 04 5. E – 04 0. E + 00 Strain –1. E – 04 Strain A C A C B D B D Figure 20: Strain of G1TB3. Figure 23: Strain of DG1TB3. 250

250 200

200 150

150 100 Load (kN)

100 50 Load (kN) G3TB1 0 50 G1TB3S100 0 5.0 E – 4 1.0 E – 3 1.5 E – 3 2.0 E – 3 0.0 E + 0 –5.0 E – 4 Strain 1. E – 04 2. E – 04 3. E – 04 4. E – 04 5. E – 04 0. E + 00 A C –1. E – 04 B D Strain Figure A C 21: Strain of G3TB1. B D

200 Figure 24: Strain of G1TB3S100.

150 and indirect loading to evaluate their shear capacity. e geometry of the FE models was taken from experimental 100 tests. All lab-measured dimensions and reinforcement details were used in FE models as shown in Figures 2–4. e Load (kN) mechanical properties of concrete adopted in FE models 50 were taken according to the experimental program. Table 9 G3TB3 presents the properties of the concrete used in this study 0 with Poisson’s ratio of 0.2 for concrete under uniaxial compression. Concrete damage plasticity model (CDM) was used to model concrete behavior, while the uniaxial stress- 5.0 E – 4 1.0 E – 3 1.5 E – 3 2.0 E – 3 2.5 E – 3 3.0 E – 3 0.0 E + 0 strain relation for steel bars was idealized as a bilinear curve, –5.0 E – 4 Strain representing elastic-plastic behavior with strain hardening, as shown in Figure 28. In the numerical simulation, a three- A C dimensional eight-node linear brick and reduced integration B D with hourglass control solid element (C3D8R) are employed Figure 22: Strain of G3TB3. to represent the concrete specimen. While three- Journal of Engineering 13

750 500 G1TB, a/d = 1.0 G3TB, a/d = 1.7

600 400

450 300

300 200 Load (kN) Load (kN)

150 100

0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 0.3 0.6 0.9 1.2 1.5 1.8 Crack Width (mm) Crack Width (mm) RCA 0% RCA 0% RCA 50% RCA 50%

(a) (b)

Figure 25: Typical crack width of indirectly loaded beams with diﬀerent RCA.

750 600 RCA 50%, a/d = 1.0 RCA 50%, a/d = 1.7 500 600

400 450 300 300 Load (kN) Load (kN) 200

150 100

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.3 0.6 0.9 1.2 1.5 1.8 Crack Width (mm) Crack Width (mm) DG1TB3 DG3TB3 G1TB3 G3TB3

(a) (b)

Figure 26: Comparison of the crack width between the directly and indirectly loaded beams with different a/d ratios. dimensional, 2-node first order truss elements (T3D2 truss) model with a different mesh size and studying its effect on are used to model the steel reinforcements. Many research the midspan deflection. Mesh size versus midspan de- studies in the literature have recommended using these flection is presented in Figure 30. e optimum mesh size elements to model the tested beams [24–26]. A typical of 25 mm gives good FE results with reasonable compu- configuration of FE models for directly and indirectly loaded tational time. beams is presented in Figure 29. e beams were directly and indirectly loaded as in the experimental tests which are 6. Comparison of STM, Experimental, and shown in Figure 7. FE Results Mesh size is an important driver of model accuracy as well as solution time since the computational costs increase is section presents a comparison between the STM cal- as the mesh is refined. Mesh size was the key parameter for culated by ACI code 318-14 and AASHTO LRFD 2012, the calibration of the FE models to determine the mesh density experimental tests, and the FEM. e ultimate load capacity, that gives convergent results with reasonable computation midspan deflection, strain in concrete and steel, and the time. Mesh refinement was addressed by running the crack pattern are discussed herein. 14 Journal of Engineering

750 RCA 50%, a/d = 1.0 600

450

300 Load (kN)

150

0 0 0.2 0.4 0.6 0.8 1 1.2 Crack width (mm) @ 50mm @ 100mm No stirrups

Figure 27: Comparison of crack width for indirectly loaded beams with diﬀerent amounts of stirrup.

fs f y Et

E 1

∈s

–fy

Figure 28: Stress-strain relation of steel reinforcement.

(a) (b)

Figure 29: e FE models conﬁguration.

6.1.UltimateLoadCapacity. e STM proposed by ACI 318- In Table 13 and Figure 31, STM underestimates the 14 and the AASHTO LRFD 2012 was used to predict the ultimate capacity of all beams compared with experimental ultimate load capacity for deep beams, as described earlier in results. e STM proposed by ACI 318-14 predicted an Section 2. STM predictions and FE results were compared ultimate strength that is lower than experimental data by an with experimental data, as presented in Table 13 and average of 38%, 44%, and 46% for GTB, DGTB, and GTBS, Figure 31. respectively. Meanwhile the STM proposed by AASHTO Journal of Engineering 15

1 Mid span deﬂection (mm)

0 300 30 3 Mesh size (mm)

Figure 30: Mesh convergence study.

Table 13: Comparison of ultimate capacity of experimental, STM, and FE results. Exp P STM STM FE Beam SN u ACI STM − Exp/Exp (%) AASHTO STM − Exp/Exp(%) FE − Exp/Exp (%) (kN) (kN) ACI (kN) AASHTO (kN) Indirectly loaded RCASCC without stirrup G1TB1 740 399 −46 399 −46 807 9 G1TB2 640 381 −40 381 −40 710 11 G1TB3 460 348 −24 348 −24 506 10 G1TB4 430 307 −29 307 −29 469 9 G2TB1 700 332 −53 248 −65 693 5 G2TB2 550 317 −42 237 −57 594 8 G2TB3 420 290 −42 216 −57 449 7 G2TB4 380 255 −33 191 −50 410 8 G3TB1 440 278 −37 156 −65 453 3 G3TB2 430 265 −38 149 −65 447 4 G3TB3 400 242 −40 136 −66 428 7 G3TB4 350 214 −39 120 −66 378 8 Indirectly loaded RCASCC with diﬀerent amounts of web reinforcement G1TB3S100 620 348 −44 348 −44 682 10 G1TB3S50 680 348 −49 348 −49 762 12 Directly loaded without stirrup and with 50% of RCA DG1TB3 620 348 −44 348 −44 682 10 DG2TB3 510 290 −43 216 −58 571 12 DG3TB3 430 242.0 −44 136 −68 469 9

900

750

600

450

300

150 Ultimate shear strength (kN)

0 G1TB3 G2TB3 G3TB3 DG1TB3 DG2TB3 DG3TB3 G1TB3S50 G1TB3S100

STM (AASHTO) Experimental STM (ACI) Finite element

Figure 31: Comparison of ultimate strength predicted by STM, experimental, and FEM results. 16 Journal of Engineering

1000 G1TB

800

600

Load (kN) 400

200

0 0 12345678 Deﬂection (mm) FE-0% FE-50% Exp-0% Exp-50%

Figure 32: Load midspan deﬂection curves for indirectly loaded beams.

700 DGTB3 600

500

400

300 Load (kN)

200

100

0 0 12345678910 Deﬂection (mm) DG1TB3 DG1TB3-FE DG2TB3 DG2TB3-FE DG3TB3 DG3TB3-FE

Figure 33: Load midspan deﬂection curves for directly loaded beams.

LRFD 2012 predicted an ultimate strength that is lower than experimental and FE results. e STM can be used to es- experimental data by an average of 53%, 57%, and 47% for timate a safer ultimate shear capacity. Even though the GTB, DGTB, and GTBS, respectively. experimental tests showed that the directly loaded beams are Generally, the FE models predicted an ultimate capacity stronger than indirectly loaded beams, the STM was unable that is slightly higher than the experimental result. is to predict such results. e experimental data were used to behavior is due to the variation in the actual material refine and calibrate the FE model. Good agreement was composition, assumed to be homogenous in the FE models. achieved between FE predictions and experimental results. However, the FE predictions showed good agreement with experimental data. FE models predicted an ultimate strength 6.2. Midspan Deflection. Figure 32 illustrates the load that is 7%, 10%, and 11% higher than the experimental data midspan deflection curves for experimental and FE results of for GTB, DGTB, and GTBS, respectively. the indirectly loaded first group of beams, G1TB. Load It can be seen from Figure 31 that the predictions yielded deflection curves for experimental and FE results of the by the STM method are more conservative than the directly loaded group, DGTB, are presented in Figure 33. It Journal of Engineering 17

350 300 250 200 150 100 Beam depth (mm) 50 0 3.0 E – 5 6.0 E – 5 9.0 E – 5 1.2 E – 4 0.0 E + 0 –1.2 E – 4 –9.0 E – 5 –6.0 E – 5 –3.0 E – 5 Concrete strain (µs) 150kN 100kN 50kN

Figure 34: FE-predicted midspan concrete strain distribution through the depth.

S, S11 (Avg: 75%) +3.906e + 02 +3.505e + 02 +3.104e + 02 +2.703e + 02 +2.302e + 02 +1.900e + 02 +1.499e + 02 +1.098e + 02 +6.971e + 01 +2.960e + 01 –1.051e + 01 –5.062e + 01 –9.074e + 01

Max: +3.906e + 02 Elem: B-STEEL-1-LIN-2-1.31 Node: 34

Min: –9.074e + 01 Elem: STR-1.18 Node: 20

Figure 35: Finite element stress for G1TB3. was observed from both Figures that the deflection predicted and 1% for directly loaded deep beams compared with the by FE models was slightly less than the corresponding experimental data. Cracking patterns obtained from the measured deflection from experimental data. Such a re- finite element analysis showed reasonable agreement with sponse is because the FE models are stiffer than the actual the failure modes obtained experimentally. beams as the FE models do not account for any variation in the actual material composition. However, the numerical data and experimental results 6.3. Strain in Concrete and Steel Reinforcement. showed very good agreement. At different loading stages, the FE-predicted midspan concrete strain distribution through predicted deflection from the FE models was lower than the the depth of the beam is presented in Figure 34. Nonlinear corresponding deflection from the experiment data. For strain distribution through the depth of the beam is observed instance, when the applied load reached 65% of the failure even at early loading stages. is finding confirms the fact load, which represents the applied service load as recom- that the nonlinear strain distribution through the depth is mended by [3, 25], the numerical models underestimated the because of the significant shear deformation. e stresses in deflection by an average of 6% for indirectly loaded beams steel reinforcement of a selected beam, G1TB3, are shown in 18 Journal of Engineering

Figure 36: Strain and crack patterns at failure load for GTB.

DG1TB3

Figure 37: Strain and crack patterns at failure load for DGTB.

Figure 35. From this figure, it can be noticed that the additional diagonal and flexural cracks. Finally, compressive maximum stress did not reach the yield strength of the main cracks appear at nearly the last applied load steps. reinforcement, which was made on purpose to achieve the failure of the compression strut before yielding the steel. 7. Summary and Conclusions Figures 36 and 37 show the experimental strain distribution along the beams. From these figures, it is indicated In this research, seventeen deep beams were prepared and that the maximum strain measurements occurred along the tested to study the shear strength of directly and indirectly load path where the inclined crack has occurred. loaded flanged self-compacted RC deep beams containing Stresses and strains in the main reinforcement were recycled concrete as coarse aggregate. Five groups were increased with the decrease of a/d because of the higher prepared, in which four groups are indirectly loaded while contribution of arch action. the fifth group is directly loaded. e parameters considered At the same load level, the increase in RCA content leads in this study are the replacement ratio of RCA, shear to a rise in both stresses and strains in steel reinforcement. span–to–effective depth (a/d) ratio, and the web rein- is response is because the beam made with a higher RCA forcement. Test results showed that all beams failed in shear has a lower stiffness and earlier cracks initiation, so the load with no local failure under load application nor over sup- transfer to steel reinforcement will occur earlier. ports. Also, the main bars properly functioned to prevent any anchorage failure. erefore, shear failure due to diagonal cracking results in splitting the beams along the 6.4. Crack Pattern. e crack in concrete initiated when the diagonal crack. e crack pattern formed a simple strut principal tensile stress developed due to the applied load configuration with a triangle shape connecting the load exceeds the tensile strength of concrete. e appearance of application area with the two supports. the cracks reflects the failure mode for the beams. Cracking It was observed from the experimental results for both, patterns obtained from the finite element analysis showed directly and indirectly, loaded beams that the compressive reasonable agreement with the failure modes obtained ex- strength, modulus of elasticity, and splitting tensile strength perimentally. Figures 36 and 37 show the experimental and were reduced by the increase of the RCA replacement ratio. FE cracking pattern for indirectly and directly loaded beams, For instance, the RCA replacement ratio increased to 25%, respectively. e number of cracks and their width were 50%, and 75%, and the compressive strength decreased by increased with increasing the RCA ratio due to the lower 44%, 13%, and 23%, respectively. Also, the splitting tensile concrete stiffness. e addition of web reinforcement leads strength decreased by 1%, 13%, and 21%, respectively, and to an increase in the load-carrying capacity of beams. the modulus of elasticity reduced by 2%, 6%, and 12%, In general, flexural cracks occur at midspan at early respectively. As a result, the measured deflection was higher loading stages. When applied loads increased, vertical when the RCA was increased. Also, a higher strain was flexural cracks spread horizontally, starting from midspan observed as the RCA was increased. e cracking and ul- toward the supports. At a higher applied load, diagonal timate capacities were decreased with the increase of the cracks appear. Increasing the applied loads induces RCA replacement ratio. For example, in beams of the first Journal of Engineering 19 group, G1TB, with RCA of 25%, 50%, and 75%, the cracking Data Availability load was decreased by 5%, 24%, and 38%, while the ultimate load was decreased by 14%, 38%, and 42%. All the data supporting the results reported in this research e cracking and ultimate loads for indirectly loaded article are available at the University of Basrah, Iraq. e beams with RCA of 50% showed an increase of 19% and data are also available from the corresponding author upon 15%, respectively, which was obtained by reducing a/d ratio request. from 1.7 to 1.0. Further, the increase in cracking and ultimate loads was 7% and 10% by reducing a/d from 1.35 to 1.0, Conflicts of Interest while for directly loaded beams with 50% of replacement, an increase of 29% and 33% of the cracking and ultimate loads e authors declare that they have no conflicts of interest was observed by reducing a/d from 1.7 to 1.0. Moreover, the regarding the publication of this paper. increase in the cracking and ultimate loads was 15% and 20% with a reduction in a/d ratio from 1.35 to 1.0. Although the presence of vertical web reinforcement References does not significantly affect the first inclined cracking loads, [1] K. N. Rahal and Y. T. Alrefaei, “Shear strength of longitu- it increases the ultimate load capacity by 48% and 35% for dinally reinforced recycled aggregate concrete beams,” En- beams with web reinforcement spaced at 50 mm and gineering Structures, vol. 145, pp. 273–282, 2017. 100 mm, respectively. e existence of web reinforcement [2] G. Wardeh and E. 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